Question: Simplify the following expression: $ q = \dfrac{4}{5} - \dfrac{n + 5}{9} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{4}{5} \times \dfrac{9}{9} = \dfrac{36}{45} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{n + 5}{9} \times \dfrac{5}{5} = \dfrac{5n + 25}{45} $ Therefore $ q = \dfrac{36}{45} - \dfrac{5n + 25}{45} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{36 - (5n + 25) }{45} $ Distribute the negative sign: $q = \dfrac{36 - 5n - 25}{45}$ $q = \dfrac{-5n + 11}{45}$